This is a great question! I think the answer to it lies in the uniqueness of works of art and in the supply side of analysis. I also think that there are some psychological principles involved. Let's look at why art is different from most other goods and services.
Most of what we buy is certainly price sensitive, and this is because much of what we buy is what economics calls substitute goods. This means that one good can easily be substituted for another. For example, if one brand of coffee goes up in price, I am likely to simply switch brands, without really suffering at all. If I want to use a tax service, if one is higher than the other, I will go for the lower-priced one, and there really won't be an appreciable difference. In a capitalistic economy, we all have plenty of choices for most things, and we exercise those choices to at least some degree based on their price depending on how elastic (very elastic, substitutes are readily chosen) or inelastic (inelastic, substitutes reluctantly chosen) they are.
However, art is not like that, is it? If I want a Monet, a cheaper Picasso is not going to do. Once you are in a largely aesthetic realm, goods are far more inelastic (substitutes chosen/ accepted extremely reluctantly) than in other markets in part because of the complex mechanism that attributes value to works of art. Art collectors are not going to be content to substitute one work of art for another. Art buyers are not shopping around for substitutes in the highly inelastic art market. Since each work of art is unique, the normal economic principles of price and demand do not apply.
There are also limitations on the artist's ability to provide a supply of artwork. For artists who are gone, of course, there are only those works that were created in their lifetimes available today. There will be no more Monets or Picassos. This limited supply drives up the price, particularly as serendipitous discoveries of lost works dwindle in today's world, which seems to have few surprises left in people's attics or basements. For living artists, though, the argument still holds true, that their production capabilities are finite. If it is fine art and not mass-produced, an artist can paint only so many paintings or create only so many sculptures. So, across the board, there is a finite supply of art, far more finite than the supply of coffee or tax services. We know that a limited supply of anything--a scarcity of any good--drives up the price of the good, and so the normal dynamics of scarcity on the supply side of economic theory applies.
Another aspect of this that occurs to me is that this is in some ways a behavioral economics question. Behavioral economics is a discipline that looks at the intersection between psychology and economics. If you know anyone who collects art or read any articles about art collectors, you will know that for some, there is something compulsive about the behavior. People will bid at an auction for a work of art not simply because they want the artwork, but also because they are caught up in winning at auction. They will often spend far more than they intended to. Auction houses encourage this by marketing their auctions with great deliberateness and by procuring what it at the "top" of the current collector's market.
As someone who teaches economics, I do think there are economic explanations for the phenomenon you speak of. But I also think that economics in and of itself does not always account for everything.
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